$ D = \left[\begin{array}{rr}2 & -2 \\ 0 & 4 \\ -1 & -2\end{array}\right]$ $ A = \left[\begin{array}{r}1 \\ 1 \\ 3\end{array}\right]$ Is $ D+ A$ defined?
Answer: In order for addition of two matrices to be defined, the matrices must have the same dimensions. If $ D$ is of dimension $( m \times  n)$ and $ A$ is of dimension $( p \times  q)$ , then for their sum to be defined: 1. $ m$ (number of rows in $ D$ ) must equal $ p$ (number of rows in $ A$ ) and 2. $ n$ (number of columns in $ D$ ) must equal $ q$ (number of columns in $ A$ Do $ D$ and $ A$ have the same number of rows? Yes Yes No Yes Do $ D$ and $ A$ have the same number of columns? No Yes No No Since $ D$ has different dimensions $(3\times2)$ from $ A$ $(3\times1)$, $ D+ A$ is not defined.